It is a heavier feel and it sure strengthens the wrist.
I'm not much of a double stroke player anyway, and if the song calls for lighter stuff I just flip it for that song, (i.e. 16ths on the hats or double strokes).
I reckon hickory is the go to wood, for its medium hardness. I got told off by my teacher for buying oak sticks years ago, said it's too hard and could stuff my wrists long term.
As far as doing damage, well, I keep my snare and toms pretty flat, and the butt stick is in my weaker hand.